I'm confused about how to decide if a number is exact or inexact. I know
that in general measurements are considered inexact, but how about
conversion factors such as 1 inch = 2.54 cm? The exactness of the
number plays a role in the number of significant digits to keep. What
other kinds of numbers are considered exact and inexact?

My calculus text defines the formula for work as W = Fd, so the work
needed to lift a 500 lb beam 30 feet would be 500 * 30 = 1500 ft-lbs.
But don't we really have to exert an upward force greater than 500
lbs in order to get the beam to move?

A stone is dropped from the top of a tower. One second later another
stone is thrown vertically downwards from the same point with a
velocity of 14 m/s. If they hit the ground together, find the height
of the tower.

When space ships get close to earth, gravity seems to affect the
occupants really fast. Why isn't the effect of gravity a gradual
occurrence? Does it have anything to do with that law about any two
bodies in the universe affecting each other... and does it have to do
with inverse relationships?